<!DOCTYPE HTML>
<html lang="zh-CN">


<head>
    <meta charset="utf-8">
    <meta name="keywords" content="机器学习算法（六）：聚类算法K-Means, blog">
    <meta name="description" content="这是我的个人网站，欢迎来访">
    <meta http-equiv="X-UA-Compatible" content="IE=edge">
    <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=no">
    <meta name="renderer" content="webkit|ie-stand|ie-comp">
    <meta name="mobile-web-app-capable" content="yes">
    <meta name="format-detection" content="telephone=no">
    <meta name="apple-mobile-web-app-capable" content="yes">
    <meta name="apple-mobile-web-app-status-bar-style" content="black-translucent">
    <!-- Global site tag (gtag.js) - Google Analytics -->


    <title>机器学习算法（六）：聚类算法K-Means | 头号咸鱼</title>
    <link rel="icon" type="image/png" href="/favicon.png">

    <link rel="stylesheet" type="text/css" href="/libs/awesome/css/all.css">
    <link rel="stylesheet" type="text/css" href="/libs/materialize/materialize.min.css">
    <link rel="stylesheet" type="text/css" href="/libs/aos/aos.css">
    <link rel="stylesheet" type="text/css" href="/libs/animate/animate.min.css">
    <link rel="stylesheet" type="text/css" href="/libs/lightGallery/css/lightgallery.min.css">
    <link rel="stylesheet" type="text/css" href="/css/matery.css">
    <link rel="stylesheet" type="text/css" href="/css/my.css">

    <script src="/libs/jquery/jquery.min.js"></script>

    <script>(function(i,s,o,g,r,a,m){i["DaoVoiceObject"]=r;i[r]=i[r]||function(){(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;a.charset="utf-8";m.parentNode.insertBefore(a,m)})(window,document,"script",('https:' == document.location.protocol ? 'https:' : 'http:') + "//widget.daovoice.io/widget/7b318e23.js","daovoice")</script>
    

<meta name="generator" content="Hexo 5.3.0">
<style>.github-emoji { position: relative; display: inline-block; width: 1.2em; min-height: 1.2em; overflow: hidden; vertical-align: top; color: transparent; }  .github-emoji > span { position: relative; z-index: 10; }  .github-emoji img, .github-emoji .fancybox { margin: 0 !important; padding: 0 !important; border: none !important; outline: none !important; text-decoration: none !important; user-select: none !important; cursor: auto !important; }  .github-emoji img { height: 1.2em !important; width: 1.2em !important; position: absolute !important; left: 50% !important; top: 50% !important; transform: translate(-50%, -50%) !important; user-select: none !important; cursor: auto !important; } .github-emoji-fallback { color: inherit; } .github-emoji-fallback img { opacity: 0 !important; }</style>
<link rel="alternate" href="/atom.xml" title="头号咸鱼" type="application/atom+xml">
</head>




<body>
    <header class="navbar-fixed">
    <nav id="headNav" class="bg-color nav-transparent">
        <div id="navContainer" class="nav-wrapper container">
            <div class="brand-logo">
                <a href="/" class="waves-effect waves-light">
                    
                    <img src="/medias/logo.png" class="logo-img" alt="LOGO">
                    
                    <span class="logo-span">头号咸鱼</span>
                </a>
            </div>
            

<a href="#" data-target="mobile-nav" class="sidenav-trigger button-collapse"><i class="fas fa-bars"></i></a>
<ul class="right nav-menu">
  
  <li class="hide-on-med-and-down nav-item">
    
    <a href="/" class="waves-effect waves-light">
      
      <i class="fas fa-home" style="zoom: 0.6;"></i>
      
      <span>首页</span>
    </a>
    
  </li>
  
  <li class="hide-on-med-and-down nav-item">
    
    <a href="/tags" class="waves-effect waves-light">
      
      <i class="fas fa-tags" style="zoom: 0.6;"></i>
      
      <span>标签</span>
    </a>
    
  </li>
  
  <li class="hide-on-med-and-down nav-item">
    
    <a href="/categories" class="waves-effect waves-light">
      
      <i class="fas fa-bookmark" style="zoom: 0.6;"></i>
      
      <span>分类</span>
    </a>
    
  </li>
  
  <li class="hide-on-med-and-down nav-item">
    
    <a href="/archives" class="waves-effect waves-light">
      
      <i class="fas fa-archive" style="zoom: 0.6;"></i>
      
      <span>归档</span>
    </a>
    
  </li>
  
  <li class="hide-on-med-and-down nav-item">
    
    <a href="/about" class="waves-effect waves-light">
      
      <i class="fas fa-user-circle" style="zoom: 0.6;"></i>
      
      <span>关于</span>
    </a>
    
  </li>
  
  <li class="hide-on-med-and-down nav-item">
    
    <a href="/contact" class="waves-effect waves-light">
      
      <i class="fas fa-comments" style="zoom: 0.6;"></i>
      
      <span>留言板</span>
    </a>
    
  </li>
  
  <li class="hide-on-med-and-down nav-item">
    
    <a href="/friends" class="waves-effect waves-light">
      
      <i class="fas fa-address-book" style="zoom: 0.6;"></i>
      
      <span>友情链接</span>
    </a>
    
  </li>
  
  <li>
    <a href="#searchModal" class="modal-trigger waves-effect waves-light">
      <i id="searchIcon" class="fas fa-search" title="搜索" style="zoom: 0.85;"></i>
    </a>
  </li>
</ul>


<div id="mobile-nav" class="side-nav sidenav">

    <div class="mobile-head bg-color">
        
        <img src="/medias/logo.png" class="logo-img circle responsive-img">
        
        <div class="logo-name">头号咸鱼</div>
        <div class="logo-desc">
            
            这是我的个人网站，欢迎来访
            
        </div>
    </div>

    

    <ul class="menu-list mobile-menu-list">
        
        <li class="m-nav-item">
	  
		<a href="/" class="waves-effect waves-light">
			
			    <i class="fa-fw fas fa-home"></i>
			
			首页
		</a>
          
        </li>
        
        <li class="m-nav-item">
	  
		<a href="/tags" class="waves-effect waves-light">
			
			    <i class="fa-fw fas fa-tags"></i>
			
			标签
		</a>
          
        </li>
        
        <li class="m-nav-item">
	  
		<a href="/categories" class="waves-effect waves-light">
			
			    <i class="fa-fw fas fa-bookmark"></i>
			
			分类
		</a>
          
        </li>
        
        <li class="m-nav-item">
	  
		<a href="/archives" class="waves-effect waves-light">
			
			    <i class="fa-fw fas fa-archive"></i>
			
			归档
		</a>
          
        </li>
        
        <li class="m-nav-item">
	  
		<a href="/about" class="waves-effect waves-light">
			
			    <i class="fa-fw fas fa-user-circle"></i>
			
			关于
		</a>
          
        </li>
        
        <li class="m-nav-item">
	  
		<a href="/contact" class="waves-effect waves-light">
			
			    <i class="fa-fw fas fa-comments"></i>
			
			留言板
		</a>
          
        </li>
        
        <li class="m-nav-item">
	  
		<a href="/friends" class="waves-effect waves-light">
			
			    <i class="fa-fw fas fa-address-book"></i>
			
			友情链接
		</a>
          
        </li>
        
        
        <li><div class="divider"></div></li>
        <li>
            <a href="https://github.com/blinkfox/hexo-theme-matery" class="waves-effect waves-light" target="_blank">
                <i class="fab fa-github-square fa-fw"></i>Fork Me
            </a>
        </li>
        
    </ul>
</div>


        </div>

        
            <style>
    .nav-transparent .github-corner {
        display: none !important;
    }

    .github-corner {
        position: absolute;
        z-index: 10;
        top: 0;
        right: 0;
        border: 0;
        transform: scale(1.1);
    }

    .github-corner svg {
        color: #0f9d58;
        fill: #fff;
        height: 64px;
        width: 64px;
    }

    .github-corner:hover .octo-arm {
        animation: a 0.56s ease-in-out;
    }

    .github-corner .octo-arm {
        animation: none;
    }

    @keyframes a {
        0%,
        to {
            transform: rotate(0);
        }
        20%,
        60% {
            transform: rotate(-25deg);
        }
        40%,
        80% {
            transform: rotate(10deg);
        }
    }
</style>

<a href="https://github.com/blinkfox/hexo-theme-matery" class="github-corner tooltipped hide-on-med-and-down" target="_blank"
   data-tooltip="Fork Me" data-position="left" data-delay="50">
    <svg viewBox="0 0 250 250" aria-hidden="true">
        <path d="M0,0 L115,115 L130,115 L142,142 L250,250 L250,0 Z"></path>
        <path d="M128.3,109.0 C113.8,99.7 119.0,89.6 119.0,89.6 C122.0,82.7 120.5,78.6 120.5,78.6 C119.2,72.0 123.4,76.3 123.4,76.3 C127.3,80.9 125.5,87.3 125.5,87.3 C122.9,97.6 130.6,101.9 134.4,103.2"
              fill="currentColor" style="transform-origin: 130px 106px;" class="octo-arm"></path>
        <path d="M115.0,115.0 C114.9,115.1 118.7,116.5 119.8,115.4 L133.7,101.6 C136.9,99.2 139.9,98.4 142.2,98.6 C133.8,88.0 127.5,74.4 143.8,58.0 C148.5,53.4 154.0,51.2 159.7,51.0 C160.3,49.4 163.2,43.6 171.4,40.1 C171.4,40.1 176.1,42.5 178.8,56.2 C183.1,58.6 187.2,61.8 190.9,65.4 C194.5,69.0 197.7,73.2 200.1,77.6 C213.8,80.2 216.3,84.9 216.3,84.9 C212.7,93.1 206.9,96.0 205.4,96.6 C205.1,102.4 203.0,107.8 198.3,112.5 C181.9,128.9 168.3,122.5 157.7,114.1 C157.9,116.9 156.7,120.9 152.7,124.9 L141.0,136.5 C139.8,137.7 141.6,141.9 141.8,141.8 Z"
              fill="currentColor" class="octo-body"></path>
    </svg>
</a>
        
    </nav>

</header>

    



<div class="bg-cover pd-header post-cover" style="background-image: url('https://cdn.jsdelivr.net/gh/liangxinxin5102/image2/cartoon01/wallhaven-nzjdxj.jpg')">
    <div class="container" style="right: 0px;left: 0px;">
        <div class="row">
            <div class="col s12 m12 l12">
                <div class="brand">
                    <h1 class="description center-align post-title">机器学习算法（六）：聚类算法K-Means</h1>
                </div>
            </div>
        </div>
    </div>
</div>




<main class="post-container content">

    
    <link rel="stylesheet" href="/libs/tocbot/tocbot.css">
<style>
    #articleContent h1::before,
    #articleContent h2::before,
    #articleContent h3::before,
    #articleContent h4::before,
    #articleContent h5::before,
    #articleContent h6::before {
        display: block;
        content: " ";
        height: 100px;
        margin-top: -100px;
        visibility: hidden;
    }

    #articleContent :focus {
        outline: none;
    }

    .toc-fixed {
        position: fixed;
        top: 64px;
    }

    .toc-widget {
        width: 345px;
        padding-left: 20px;
    }

    .toc-widget .toc-title {
        padding: 35px 0 15px 17px;
        font-size: 1.5rem;
        font-weight: bold;
        line-height: 1.5rem;
    }

    .toc-widget ol {
        padding: 0;
        list-style: none;
    }

    #toc-content {
        padding-bottom: 30px;
        overflow: auto;
    }

    #toc-content ol {
        padding-left: 10px;
    }

    #toc-content ol li {
        padding-left: 10px;
    }

    #toc-content .toc-link:hover {
        color: #42b983;
        font-weight: 700;
        text-decoration: underline;
    }

    #toc-content .toc-link::before {
        background-color: transparent;
        max-height: 25px;

        position: absolute;
        right: 23.5vw;
        display: block;
    }

    #toc-content .is-active-link {
        color: #42b983;
    }

    #floating-toc-btn {
        position: fixed;
        right: 15px;
        bottom: 76px;
        padding-top: 15px;
        margin-bottom: 0;
        z-index: 998;
    }

    #floating-toc-btn .btn-floating {
        width: 48px;
        height: 48px;
    }

    #floating-toc-btn .btn-floating i {
        line-height: 48px;
        font-size: 1.4rem;
    }
</style>
<div class="row">
    <div id="main-content" class="col s12 m12 l9">
        <!-- 文章内容详情 -->
<div id="artDetail">
    <div class="card">
        <div class="card-content article-info">
            <div class="row tag-cate">
                <div class="col s7">
                    
                    <div class="article-tag">
                        
                            <a href="/tags/%E7%AE%97%E6%B3%95/">
                                <span class="chip bg-color">算法</span>
                            </a>
                        
                            <a href="/tags/%E6%B0%B4/">
                                <span class="chip bg-color">水</span>
                            </a>
                        
                    </div>
                    
                </div>
                <div class="col s5 right-align">
                    
                    <div class="post-cate">
                        <i class="fas fa-bookmark fa-fw icon-category"></i>
                        
                            <a href="/categories/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/" class="post-category">
                                机器学习
                            </a>
                        
                    </div>
                    
                </div>
            </div>

            <div class="post-info">
                
                <div class="post-date info-break-policy">
                    <i class="far fa-calendar-minus fa-fw"></i>发布日期:&nbsp;&nbsp;
                    2021-03-15
                </div>
                

                
                <div class="post-date info-break-policy">
                    <i class="far fa-calendar-check fa-fw"></i>更新日期:&nbsp;&nbsp;
                    2021-03-16
                </div>
                

                
                <div class="info-break-policy">
                    <i class="far fa-file-word fa-fw"></i>文章字数:&nbsp;&nbsp;
                    2.8k
                </div>
                

                
                <div class="info-break-policy">
                    <i class="far fa-clock fa-fw"></i>阅读时长:&nbsp;&nbsp;
                    13 分
                </div>
                

                
                    <div id="busuanzi_container_page_pv" class="info-break-policy">
                        <i class="far fa-eye fa-fw"></i>阅读次数:&nbsp;&nbsp;
                        <span id="busuanzi_value_page_pv"></span>
                    </div>
				
            </div>
        </div>
        <hr class="clearfix">

        
        <!-- 是否加载使用自带的 prismjs. -->
        <link rel="stylesheet" href="/libs/prism/prism.css">
        

        

        <div class="card-content article-card-content">
            <div id="articleContent">
                <blockquote>
<p>这一系列的笔记水得很，开始兴致冲冲，潦草结束都算不上，半途而废。虽然这样做有点帮助，但是最重要的还是<strong>思考实践</strong>，不是为了做笔记而做笔记，这一波笔记，到最后简直要吐了，不知道为了什么，吐得我几天都不想碰了。<strong>参考菜菜视频教程</strong>，还不如直接看pdf。等我做了好web项目再战机器学习。</p>
</blockquote>
<h2 id="一、概述"><a href="#一、概述" class="headerlink" title="一、概述"></a>一、概述</h2><h4 id="1-无监督学习与聚类算法"><a href="#1-无监督学习与聚类算法" class="headerlink" title="1.无监督学习与聚类算法"></a>1.无监督学习与聚类算法</h4><p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310005114.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310005127.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310005148.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310005201.png"></p>
<h4 id="2-KMeans"><a href="#2-KMeans" class="headerlink" title="2.KMeans"></a>2.KMeans</h4><p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310005227.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310005241.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310005259.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310005311.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310005325.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310005350.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310005411.png"></p>
<h2 id="二、sklearn-cluster-KMeans"><a href="#二、sklearn-cluster-KMeans" class="headerlink" title="二、sklearn.cluster.KMeans"></a>二、sklearn.cluster.KMeans</h2><pre class="line-numbers language-none"><code class="language-none">class sklearn.cluster.KMeans (n_clusters=8, init=’k-means++’, n_init=10, max_iter=300, tol=0.0001,
precompute_distances=’auto’, verbose=0, random_state=None, copy_x=True, n_jobs=None, algorithm=’auto’)<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310005458.png"></p>
<pre class="line-numbers language-none"><code class="language-none">from sklearn.datasets import make_blobs
import matplotlib.pyplot as plt

#自己创建数据集
X, y = make_blobs(n_samples=500,n_features=2,centers=4,random_state=1)

X.shape
# (500, 2)

y.shape
# (500,)

fig, ax1 = plt.subplots(1)
ax1.scatter(X[:, 0], X[:, 1]#.scatter散点图
            ,marker='o' #点的形状
            ,s=8 #点的大小
           )
plt.show()<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310005616.png"></p>
<pre class="line-numbers language-none"><code class="language-none">#如果我们想要看见这个点的分布，怎么办？
color = ["red","pink","orange","gray"]
fig, ax1 = plt.subplots(1)

for i in range(4):
    ax1.scatter(X[y==i, 0], X[y==i, 1]
            ,marker='o' #点的形状
            ,s=8 #点的大小
            ,c=color[i]
           )
plt.show()<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310005838.png"></p>
<blockquote>
<p>基于这个分布，我们来使用Kmeans进行聚类。首先，我们要猜测一下，这个数据中有几簇？</p>
</blockquote>
<pre class="line-numbers language-none"><code class="language-none">from sklearn.cluster import KMeans

n_clusters = 3

cluster = KMeans(n_clusters=n_clusters,random_state=0).fit(X)

#重要属性Labels_，查看聚好的类别，每个样本所对应的类
y_pred = cluster.labels_
y_pred

#KMeans因为并不需要建立模型或者预测结果，因此我们只需要fit就能够得到聚类结果了
#KMeans也有接口predict和fit_predict，表示学习数据X并对X的类进行预测
#但所得到的结果和我们不调用predict，直接fit之后调用属性labels一模一伴
pre = cluster.fit_predict(X)
pre

pre == y_pred#全都是True

#我们什么时候需要predict呢？当数据量太大的时候！
#其实我们不必使用所有的数据来寻找质心，少量的数据就可以帮助我们确定质心了
#当我们数据量非常大的时候，我们可以使用部分数据来帮助我们确认质心
#剩下的数据的聚类结果，使用predict来调用
cluster_smallsub = KMeans(n_clusters=n_clusters, random_state=0).fit(X[:200])

y_pred_ = cluster_smallsub.predict(X)

y_pred_

y_pred == y_pred_#数据量非常大的时候，效果会好
#但从运行得出这样的结果，肯定与直接fit全部数据会不一致。有时候，当我们不要求那么精确，或者我们的数据量实在太大，那我们可以使用这种方法，使用接口predict
#如果数据量还行，不是特别大，直接使用fit之后调用属性.labels_提出来

#重要属性cLuster_centers_，查看质心
centroid = cluster.cluster_centers_
centroid

centroid.shape
# (3, 2)

#重要属性inertia_，查看总距离平方和
inertia = cluster.inertia_
inertia
# 1903.4503741659223

color = ["red","pink","orange","gray"]

fig, ax1 = plt.subplots(1)

for i in range(n_clusters):
    ax1.scatter(X[y_pred==i, 0], X[y_pred==i, 1]
            ,marker='o' #点的形状
            ,s=8 #点的大小
            ,c=color[i]
           )
    
ax1.scatter(centroid[:,0],centroid[:,1]
           ,marker="x"
           ,s=15
           ,c="black")
plt.show()<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310010054.png"></p>
<pre class="line-numbers language-none"><code class="language-none">#如果我们把猜测的羡数换成4，Inertia会怎么样？
n_clusters = 4
cluster_ = KMeans(n_clusters=n_clusters, random_state=0).fit(X)
inertia_ = cluster_.inertia_
inertia_
# 908.3855684760613

n_clusters = 5
cluster_ = KMeans(n_clusters=n_clusters, random_state=0).fit(X)
inertia_ = cluster_.inertia_
inertia_
# 811.0841324482415

n_clusters = 6
cluster_ = KMeans(n_clusters=n_clusters, random_state=0).fit(X)
inertia_ = cluster_.inertia_
inertia_
# 733.153835008308<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310010202.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310010217.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310010226.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310010237.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310010249.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310010301.png"></p>
<pre class="line-numbers language-none"><code class="language-none">from sklearn.metrics import silhouette_score
from sklearn.metrics import silhouette_samples

X.shape#(500, 2)
y_pred #.labels_

silhouette_score(X,y_pred)
# 0.5882004012129721

silhouette_score(X,cluster_.labels_) #分4簇的确比分3簇效果要好
# 0.6505186632729437

silhouette_score(X,cluster_.labels_) #分5簇
# 0.5746932321727456

silhouette_score(X,cluster_.labels_) #分6簇
# 0.5150064498560357

# silhouette_samples(X,y_pred)
silhouette_samples(X,y_pred).shape#(500,)
silhouette_samples(X,y_pred).mean()
# 0.5882004012129721<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310010438.png"></p>
<pre class="line-numbers language-none"><code class="language-none">from sklearn.metrics import calinski_harabaz_score

X
y_pred

calinski_harabaz_score(X, y_pred)
# 1809.991966958033<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<blockquote>
<p>虽然calinski-Harabaz指数没有界，在凸型的数据上的聚类也会表现虚高。但是比起轮廓系数，它有一个巨大的优 点，就是计算非常快速。之前我们使用过魔法命令%%timeit来计算一个命令的运算时间，今天我们来选择另一种 方法：时间戳计算运行时间。</p>
</blockquote>
<pre class="line-numbers language-none"><code class="language-none">from time import time
#time（）：记下每一次time（）这一行命令时的时间戳
#时间戳是一行数字，用来记录此时此刻的时间
t0 = time()
calinski_harabaz_score(X, y_pred)
time() - t0#0.0015027523040771484

t0 = time()
silhouette_score(X,y_pred)
time() - t0#0.007976055145263672

t0
# 1544880610.0802236

#时间戳可以通过datetime中的函数fromtimestamp转换成真正的时间格式
import datetime
datetime.datetime.fromtimestamp(t0).strftime("%Y-%m-%d %H:%M:%S")
# '2018-12-15 21:30:10'<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310010611.png"></p>
<pre class="line-numbers language-none"><code class="language-none">from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_samples, silhouette_score
import matplotlib.pyplot as plt
import matplotlib.cm as cm #colormap
import numpy as np
import pandas as pd

n_clusters = 4
fig, (ax1, ax2) = plt.subplots(1, 2)
fig.set_size_inches(18,7)
ax1.set_xlim([-0.1, 1])
ax1.set_ylim([0, X.shape[0] + (n_clusters + 1) * 10])
clusterer = KMeans(n_clusters=n_clusters, random_state=10).fit(X)
cluster_labels = clusterer.labels_
silhouette_avg = silhouette_score(X, cluster_labels)
print("For n_clusters =", n_clusters,
      "The average silhouette_score is :", silhouette_avg)

sample_silhouette_values = silhouette_samples(X, cluster_labels)

y_lower = 10

for i in range(n_clusters):
    ith_cluster_silhouette_values = sample_silhouette_values[cluster_labels == i]
    ith_cluster_silhouette_values.sort()
    size_cluster_i = ith_cluster_silhouette_values.shape[0]
    y_upper = y_lower + size_cluster_i
    color = cm.nipy_spectral(float(i)/n_clusters)
    
    ax1.fill_betweenx(np.arange(y_lower, y_upper)
                      ,ith_cluster_silhouette_values
                      ,facecolor=color
                      ,alpha=0.7
                     )

    ax1.text(-0.05
             , y_lower + 0.5 * size_cluster_i
             , str(i))

    y_lower = y_upper + 10
    
ax1.set_title("The silhouette plot for the various clusters.")
ax1.set_xlabel("The silhouette coefficient values")
ax1.set_ylabel("Cluster label")

ax1.axvline(x=silhouette_avg, color="red", linestyle="--")

ax1.set_yticks([])

ax1.set_xticks([-0.1, 0, 0.2, 0.4, 0.6, 0.8, 1])

colors = cm.nipy_spectral(cluster_labels.astype(float) / n_clusters)

ax2.scatter(X[:, 0], X[:, 1]
            ,marker='o'
            ,s=8
            ,c=colors
           )

centers = clusterer.cluster_centers_
# Draw white circles at cluster centers
ax2.scatter(centers[:, 0], centers[:, 1], marker='x',
            c="red", alpha=1, s=200)

ax2.set_title("The visualization of the clustered data.")
ax2.set_xlabel("Feature space for the 1st feature")
ax2.set_ylabel("Feature space for the 2nd feature")

plt.suptitle(("Silhouette analysis for KMeans clustering on sample data"
              "with n_clusters = %d" % n_clusters),
             fontsize=14, fontweight='bold')
plt.show()<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310010800.png"></p>
<blockquote>
<p>将上述过程包装成一个循环，可以得到：</p>
</blockquote>
<pre class="line-numbers language-none"><code class="language-none">from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_samples, silhouette_score

import matplotlib.pyplot as plt
import matplotlib.cm as cm
import numpy as np

for n_clusters in [2,3,4,5,6,7]:
    n_clusters = n_clusters
    fig, (ax1, ax2) = plt.subplots(1, 2)
    fig.set_size_inches(18, 7)
    ax1.set_xlim([-0.1, 1])
    ax1.set_ylim([0, X.shape[0] + (n_clusters + 1) * 10])
    clusterer = KMeans(n_clusters=n_clusters, random_state=10).fit(X)
    cluster_labels = clusterer.labels_
    silhouette_avg = silhouette_score(X, cluster_labels)
    print("For n_clusters =", n_clusters,
          "The average silhouette_score is :", silhouette_avg)
    sample_silhouette_values = silhouette_samples(X, cluster_labels)
    y_lower = 10
    for i in range(n_clusters):
        ith_cluster_silhouette_values = sample_silhouette_values[cluster_labels == i]
        ith_cluster_silhouette_values.sort()
        size_cluster_i = ith_cluster_silhouette_values.shape[0]
        y_upper = y_lower + size_cluster_i
        color = cm.nipy_spectral(float(i)/n_clusters)
        ax1.fill_betweenx(np.arange(y_lower, y_upper)
                          ,ith_cluster_silhouette_values
                          ,facecolor=color
                          ,alpha=0.7
                         )
        ax1.text(-0.05
                 , y_lower + 0.5 * size_cluster_i
                 , str(i))
        y_lower = y_upper + 10

    ax1.set_title("The silhouette plot for the various clusters.")
    ax1.set_xlabel("The silhouette coefficient values")
    ax1.set_ylabel("Cluster label")
    ax1.axvline(x=silhouette_avg, color="red", linestyle="--")
    ax1.set_yticks([])
    ax1.set_xticks([-0.1, 0, 0.2, 0.4, 0.6, 0.8, 1])

    colors = cm.nipy_spectral(cluster_labels.astype(float) / n_clusters)
    ax2.scatter(X[:, 0], X[:, 1]
                ,marker='o'
                ,s=8
                ,c=colors
               )
    centers = clusterer.cluster_centers_
    # Draw white circles at cluster centers
    ax2.scatter(centers[:, 0], centers[:, 1], marker='x',
                c="red", alpha=1, s=200)
    
    ax2.set_title("The visualization of the clustered data.")
    ax2.set_xlabel("Feature space for the 1st feature")
    ax2.set_ylabel("Feature space for the 2nd feature")

    plt.suptitle(("Silhouette analysis for KMeans clustering on sample data "
                  "with n_clusters = %d" % n_clusters),
                 fontsize=14, fontweight='bold')
    plt.show()<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310010847.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310010901.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310010926.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310010941.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310010957.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310011049.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310011105.png"></p>
<pre class="line-numbers language-none"><code class="language-none">X.shape
# (500, 2)

y.shape
# (500,)

plus = KMeans(n_clusters = 10).fit(X)
plus.n_iter_
# 10

random = KMeans(n_clusters = 10,init="random",random_state=420).fit(X)
random.n_iter_
# 19<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310011222.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310011230.png"></p>
<pre class="line-numbers language-none"><code class="language-none">random = KMeans(n_clusters = 10,init="random",max_iter=10,random_state=420).fit(X)
y_pred_max10 = random.labels_
silhouette_score(X,y_pred_max10)
# 0.3952586444034157

random = KMeans(n_clusters = 10,init="random",max_iter=20,random_state=420).fit(X)
y_pred_max20 = random.labels_
silhouette_score(X,y_pred_max20)
# 0.3401504537571701<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310011325.png"></p>
<h4 id="函数cluster-k-means"><a href="#函数cluster-k-means" class="headerlink" title="函数cluster.k_means"></a>函数cluster.k_means</h4><pre class="line-numbers language-none"><code class="language-none">sklearn.cluster.k_means (X, n_clusters, sample_weight=None, init=’k-means++’, precompute_distances=’auto’,
n_init=10, max_iter=300, verbose=False, tol=0.0001, random_state=None, copy_x=True, n_jobs=None,
algorithm=’auto’, return_n_iter=False)<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span></span></code></pre>
<ul>
<li>函数k_means的用法其实和类非常相似，不过函数是输入一系列值，而直接返回结果。一次性地，函数k_means会 依次返回质心，每个样本对应的簇的标签，inertia以及最佳迭代次数。</li>
</ul>
<pre class="line-numbers language-none"><code class="language-none">from sklearn.cluster import k_means

k_means(X,4,return_n_iter=False)<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span></span></code></pre>
<h2 id="三、-案例：聚类算法用于降维，KMeans的矢量量化应用"><a href="#三、-案例：聚类算法用于降维，KMeans的矢量量化应用" class="headerlink" title="三、 案例：聚类算法用于降维，KMeans的矢量量化应用"></a>三、 案例：聚类算法用于降维，KMeans的矢量量化应用</h2><p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310011430.png"></p>
<ol>
<li>导入库</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">import numpy as np
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
from sklearn.metrics import pairwise_distances_argmin
    #对两个序列中的点进行距离匹配的函数
from sklearn.datasets import load_sample_image
    #导入图片数据所用的类
from sklearn.utils import shuffle #洗牌<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<ol start="2">
<li> 导入数据，探索数据</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none"># 实例化，导入颐和园的图片
china = load_sample_image("china.jpg")

china

#查看数据类型
china.dtype

china.shape
#长度 x 宽度 x 像素 &gt; 三个数决定的颜色

china[0][0]

#包含多少种不同的颜色?
newimage = china.reshape((427 * 640,3))

newimage.shape
# (273280, 3)

import pandas as pd
pd.DataFrame(newimage).drop_duplicates().shape
# (96615, 3)
#我们现在有9W多种颜色

# 图像可视化
plt.figure(figsize=(15,15))
plt.imshow(china) #导入3维数组形成的图片

#查看模块中的另一张图片
flower = load_sample_image("flower.jpg")
plt.figure(figsize=(15,15))
plt.imshow(flower)<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310011712.png"></p>
<pre class="line-numbers language-none"><code class="language-none">n_clusters = 64

china = np.array(china, dtype=np.float64) / china.max()
w, h, d = original_shape = tuple(china.shape)
assert d == 3
image_array = np.reshape(china, (w * h, d))

#plt.imshow在浮点数上表现非常优异，在这里我们把china中的数据，转换为浮点数，压缩到[0,1]之间
china = np.array(china, dtype=np.float64) / china.max()

(china &lt; 0).sum()

(china &gt; 1).sum()

#把china从图像格式，转换成矩阵格式
w, h, d = original_shape = tuple(china.shape)
w
# 427
h
# 640
d
# 3

assert d == 3
#assert相当于 raise error if not，表示为，“不为True就报错”
#要求d必须等于3，如果不等于，就报错

#展示assert的功能
d_ = 3
assert d_ == 3, "一个格子中特征数不等于3"
image_array = np.reshape(china, (w * h, d)) #reshape是改变结构
image_array

image_array.shape
# (273280, 3)

#np.reshape(a, newshape, order='C'), reshape函数的第一个参数a是要改变结构的对象，第二个参数是要改变的新结构
#展示np.reshape的效果
a = np.random.random((2,4))
a.shape
# (2, 4)
a.reshape((4,2)) == np.reshape(a,(4,2))
np.reshape(a,(2,2,2)).shape
# (2, 2, 2)

np.reshape(a,(8,1))
np.reshape(a,(1,4))

#无论有几维，只要维度之间相乘后的总数据量不变，维度可以随意变换
a.shape
# (2, 4)<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<ol start="4">
<li>对数据进行K-Means的矢量量化</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">#首先，先使用1000个数据来找出质心
image_array_sample = shuffle(image_array, random_state=0)[:1000]
kmeans = KMeans(n_clusters=n_clusters, random_state=0).fit(image_array_sample)

kmeans.cluster_centers_.shape
# (64, 3)

#找出质心之后，按照已存在的质心对所有数据进行聚类
labels = kmeans.predict(image_array)
labels.shape
# (273280,)

set(labels)

#使用质心来替换所有的样本
image_kmeans = image_array.copy()

image_kmeans #27W个样本点，9W多种不同的颜色（像素点）

labels #这27W个样本点所对应的簇的质心的索引
# 62

kmeans.cluster_centers_[labels[0]]
# array([0.73524384, 0.82021116, 0.91925591])

for i in range(w*h):
    image_kmeans[i] = kmeans.cluster_centers_[labels[i]]
    
#查看生成的新图片信息
image_kmeans.shape
# (273280, 3)

pd.DataFrame(image_kmeans).drop_duplicates().shape
# (64, 3)

#恢复图片的结构
image_kmeans = image_kmeans.reshape(w,h,d)
image_kmeans.shape
# (427, 640, 3)<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<ol start="5">
<li>对数据进行随机的矢量量化</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">centroid_random = shuffle(image_array, random_state=0)[:n_clusters]
centroid_random.shape
# (64, 3)

labels_random = pairwise_distances_argmin(centroid_random,image_array,axis=0)

#函数pairwise_distances_argmin(x1,x2,axis) #x1和x2分别是序列
#用来计算x2中的每个样本到x1中的每个样本点的距离，并返回和x2相同形状的，x1中对应的最近的样本点的索引
labels_random.shape
# (273280,)

labels_random
# array([55, 55, 55, ..., 52, 60, 60], dtype=int64)

len(set(labels_random))
# 64

#使用随机质心来替换所有样本
image_random = image_array.copy()
for i in range(w*h):
    image_random[i] = centroid_random[labels_random[i]]
#恢复图片的结构
image_random = image_random.reshape(w,h,d)
image_random.shape
# (427, 640, 3)

<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<ol start="6">
<li>将原图，按KMeans矢量量化和随机矢量量化的图像绘制出来</li>
</ol>
<pre class="line-numbers language-none"><code class="language-none">plt.figure(figsize=(10,10))
plt.axis('off')
plt.title('Original image (96,615 colors)')
plt.imshow(china)

plt.figure(figsize=(10,10))
plt.axis('off')
plt.title('Quantized image (64 colors, K-Means)')
plt.imshow(image_kmeans)

plt.figure(figsize=(10,10))
plt.axis('off')
plt.title('Quantized image (64 colors, Random)')
plt.imshow(image_random)
plt.show()<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<h2 id="四、附录"><a href="#四、附录" class="headerlink" title="四、附录"></a>四、附录</h2><p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310211002.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310211017.png"></p>
<p><img src="https://gitee.com/liangxinixn/blog002/raw/master/image01/20210310211030.png"></p>

                
            </div>
            <hr/>

            

    <div class="reprint" id="reprint-statement">
        
            <div class="reprint__author">
                <span class="reprint-meta" style="font-weight: bold;">
                    <i class="fas fa-user">
                        文章作者:
                    </i>
                </span>
                <span class="reprint-info">
                    <a href="/about" rel="external nofollow noreferrer">lxx</a>
                </span>
            </div>
            <div class="reprint__type">
                <span class="reprint-meta" style="font-weight: bold;">
                    <i class="fas fa-link">
                        文章链接:
                    </i>
                </span>
                <span class="reprint-info">
                    <a href="http://xinxinliang.github.io/2021/03/15/ji-qi-xue-xi-suan-fa-liu-ju-lei-suan-fa-k-means/">http://xinxinliang.github.io/2021/03/15/ji-qi-xue-xi-suan-fa-liu-ju-lei-suan-fa-k-means/</a>
                </span>
            </div>
            <div class="reprint__notice">
                <span class="reprint-meta" style="font-weight: bold;">
                    <i class="fas fa-copyright">
                        版权声明:
                    </i>
                </span>
                <span class="reprint-info">
                    本博客所有文章除特別声明外，均采用
                    <a href="https://creativecommons.org/licenses/by/4.0/deed.zh" rel="external nofollow noreferrer" target="_blank">CC BY 4.0</a>
                    许可协议。转载请注明来源
                    <a href="/about" target="_blank">lxx</a>
                    !
                </span>
            </div>
        
    </div>

    <script async defer>
      document.addEventListener("copy", function (e) {
        let toastHTML = '<span>复制成功，请遵循本文的转载规则</span><button class="btn-flat toast-action" onclick="navToReprintStatement()" style="font-size: smaller">查看</a>';
        M.toast({html: toastHTML})
      });

      function navToReprintStatement() {
        $("html, body").animate({scrollTop: $("#reprint-statement").offset().top - 80}, 800);
      }
    </script>



            <div class="tag_share" style="display: block;">
                <div class="post-meta__tag-list" style="display: inline-block;">
                    
                        <div class="article-tag">
                            
                                <a href="/tags/%E7%AE%97%E6%B3%95/">
                                    <span class="chip bg-color">算法</span>
                                </a>
                            
                                <a href="/tags/%E6%B0%B4/">
                                    <span class="chip bg-color">水</span>
                                </a>
                            
                        </div>
                    
                </div>
                <div class="post_share" style="zoom: 80%; width: fit-content; display: inline-block; float: right; margin: -0.15rem 0;">
                    <link rel="stylesheet" type="text/css" href="/libs/share/css/share.min.css">
<div id="article-share">

    
    <div class="social-share" data-sites="twitter,facebook,google,qq,qzone,wechat,weibo,douban,linkedin" data-wechat-qrcode-helper="<p>微信扫一扫即可分享！</p>"></div>
    <script src="/libs/share/js/social-share.min.js"></script>
    

    

</div>

                </div>
            </div>
            
                <style>
    #reward {
        margin: 40px 0;
        text-align: center;
    }

    #reward .reward-link {
        font-size: 1.4rem;
        line-height: 38px;
    }

    #reward .btn-floating:hover {
        box-shadow: 0 6px 12px rgba(0, 0, 0, 0.2), 0 5px 15px rgba(0, 0, 0, 0.2);
    }

    #rewardModal {
        width: 320px;
        height: 350px;
    }

    #rewardModal .reward-title {
        margin: 15px auto;
        padding-bottom: 5px;
    }

    #rewardModal .modal-content {
        padding: 10px;
    }

    #rewardModal .close {
        position: absolute;
        right: 15px;
        top: 15px;
        color: rgba(0, 0, 0, 0.5);
        font-size: 1.3rem;
        line-height: 20px;
        cursor: pointer;
    }

    #rewardModal .close:hover {
        color: #ef5350;
        transform: scale(1.3);
        -moz-transform:scale(1.3);
        -webkit-transform:scale(1.3);
        -o-transform:scale(1.3);
    }

    #rewardModal .reward-tabs {
        margin: 0 auto;
        width: 210px;
    }

    .reward-tabs .tabs {
        height: 38px;
        margin: 10px auto;
        padding-left: 0;
    }

    .reward-content ul {
        padding-left: 0 !important;
    }

    .reward-tabs .tabs .tab {
        height: 38px;
        line-height: 38px;
    }

    .reward-tabs .tab a {
        color: #fff;
        background-color: #ccc;
    }

    .reward-tabs .tab a:hover {
        background-color: #ccc;
        color: #fff;
    }

    .reward-tabs .wechat-tab .active {
        color: #fff !important;
        background-color: #22AB38 !important;
    }

    .reward-tabs .alipay-tab .active {
        color: #fff !important;
        background-color: #019FE8 !important;
    }

    .reward-tabs .reward-img {
        width: 210px;
        height: 210px;
    }
</style>

<div id="reward">
    <a href="#rewardModal" class="reward-link modal-trigger btn-floating btn-medium waves-effect waves-light red">赏</a>

    <!-- Modal Structure -->
    <div id="rewardModal" class="modal">
        <div class="modal-content">
            <a class="close modal-close"><i class="fas fa-times"></i></a>
            <h4 class="reward-title">你的赏识是我前进的动力</h4>
            <div class="reward-content">
                <div class="reward-tabs">
                    <ul class="tabs row">
                        <li class="tab col s6 alipay-tab waves-effect waves-light"><a href="#alipay">支付宝</a></li>
                        <li class="tab col s6 wechat-tab waves-effect waves-light"><a href="#wechat">微 信</a></li>
                    </ul>
                    <div id="alipay">
                        <img src="https://gitee.com/liangxinixn/guitar/raw/master/image01/20200726220206.png" class="reward-img" alt="支付宝打赏二维码">
                    </div>
                    <div id="wechat">
                        <img src="https://gitee.com/liangxinixn/guitar/raw/master/image01/20200726220308.png" class="reward-img" alt="微信打赏二维码">
                    </div>
                </div>
            </div>
        </div>
    </div>
</div>

<script>
    $(function () {
        $('.tabs').tabs();
    });
</script>

            
        </div>
    </div>

    

    

    

    

    

    

    

    

    

<article id="prenext-posts" class="prev-next articles">
    <div class="row article-row">
        
        <div class="article col s12 m6" data-aos="fade-up">
            <div class="article-badge left-badge text-color">
                <i class="fas fa-chevron-left"></i>&nbsp;上一篇</div>
            <div class="card">
                <a href="/2021/03/15/ji-qi-xue-xi-suan-fa-wan-zhi-chi-xiang-liang-ji-svm/">
                    <div class="card-image">
                        
                        <img src="https://cdn.jsdelivr.net/gh/liangxinxin5102/image2/cartoon01/wallhaven-odlp9m.jpg" class="responsive-img" alt="机器学习算法（完）：支持向量机SVM">
                        
                        <span class="card-title">机器学习算法（完）：支持向量机SVM</span>
                    </div>
                </a>
                <div class="card-content article-content">
                    <div class="summary block-with-text">
                        
                            
                        
                    </div>
                    <div class="publish-info">
                        <span class="publish-date">
                            <i class="far fa-clock fa-fw icon-date"></i>2021-03-15
                        </span>
                        <span class="publish-author">
                            
                            <i class="fas fa-bookmark fa-fw icon-category"></i>
                            
                            <a href="/categories/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/" class="post-category">
                                    机器学习
                                </a>
                            
                            
                        </span>
                    </div>
                </div>
                
                <div class="card-action article-tags">
                    
                    <a href="/tags/%E7%AE%97%E6%B3%95/">
                        <span class="chip bg-color">算法</span>
                    </a>
                    
                    <a href="/tags/%E6%B0%B4/">
                        <span class="chip bg-color">水</span>
                    </a>
                    
                </div>
                
            </div>
        </div>
        
        
        <div class="article col s12 m6" data-aos="fade-up">
            <div class="article-badge right-badge text-color">
                下一篇&nbsp;<i class="fas fa-chevron-right"></i>
            </div>
            <div class="card">
                <a href="/2021/03/15/ji-qi-xue-xi-suan-fa-wu-luo-ji-hui-gui/">
                    <div class="card-image">
                        
                        <img src="https://cdn.jsdelivr.net/gh/liangxinxin5102/image2/cartoon01/wallhaven-nrrlqn.jpg" class="responsive-img" alt="机器学习算法（五）：逻辑回归">
                        
                        <span class="card-title">机器学习算法（五）：逻辑回归</span>
                    </div>
                </a>
                <div class="card-content article-content">
                    <div class="summary block-with-text">
                        
                            
                        
                    </div>
                    <div class="publish-info">
                            <span class="publish-date">
                                <i class="far fa-clock fa-fw icon-date"></i>2021-03-15
                            </span>
                        <span class="publish-author">
                            
                            <i class="fas fa-bookmark fa-fw icon-category"></i>
                            
                            <a href="/categories/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/" class="post-category">
                                    机器学习
                                </a>
                            
                            
                        </span>
                    </div>
                </div>
                
                <div class="card-action article-tags">
                    
                    <a href="/tags/%E7%AE%97%E6%B3%95/">
                        <span class="chip bg-color">算法</span>
                    </a>
                    
                    <a href="/tags/%E6%B0%B4/">
                        <span class="chip bg-color">水</span>
                    </a>
                    
                </div>
                
            </div>
        </div>
        
    </div>
</article>

</div>


<script>
    $('#articleContent').on('copy', function (e) {
        // IE8 or earlier browser is 'undefined'
        if (typeof window.getSelection === 'undefined') return;

        var selection = window.getSelection();
        // if the selection is short let's not annoy our users.
        if (('' + selection).length < Number.parseInt('120')) {
            return;
        }

        // create a div outside of the visible area and fill it with the selected text.
        var bodyElement = document.getElementsByTagName('body')[0];
        var newdiv = document.createElement('div');
        newdiv.style.position = 'absolute';
        newdiv.style.left = '-99999px';
        bodyElement.appendChild(newdiv);
        newdiv.appendChild(selection.getRangeAt(0).cloneContents());

        // we need a <pre> tag workaround.
        // otherwise the text inside "pre" loses all the line breaks!
        if (selection.getRangeAt(0).commonAncestorContainer.nodeName === 'PRE') {
            newdiv.innerHTML = "<pre>" + newdiv.innerHTML + "</pre>";
        }

        var url = document.location.href;
        newdiv.innerHTML += '<br />'
            + '来源: 头号咸鱼<br />'
            + '文章作者: lxx<br />'
            + '文章链接: <a href="' + url + '">' + url + '</a><br />'
            + '本文章著作权归作者所有，任何形式的转载都请注明出处。';

        selection.selectAllChildren(newdiv);
        window.setTimeout(function () {bodyElement.removeChild(newdiv);}, 200);
    });
</script>


<!-- 代码块功能依赖 -->
<script type="text/javascript" src="/libs/codeBlock/codeBlockFuction.js"></script>

<!-- 代码语言 -->

<script type="text/javascript" src="/libs/codeBlock/codeLang.js"></script>


<!-- 代码块复制 -->

<script type="text/javascript" src="/libs/codeBlock/codeCopy.js"></script>


<!-- 代码块收缩 -->

<script type="text/javascript" src="/libs/codeBlock/codeShrink.js"></script>


    </div>
    <div id="toc-aside" class="expanded col l3 hide-on-med-and-down">
        <div class="toc-widget card" style="background-color: white;">
            <div class="toc-title"><i class="far fa-list-alt"></i>&nbsp;&nbsp;目录</div>
            <div id="toc-content"></div>
        </div>
    </div>
</div>

<!-- TOC 悬浮按钮. -->

<div id="floating-toc-btn" class="hide-on-med-and-down">
    <a class="btn-floating btn-large bg-color">
        <i class="fas fa-list-ul"></i>
    </a>
</div>


<script src="/libs/tocbot/tocbot.min.js"></script>
<script>
    $(function () {
        tocbot.init({
            tocSelector: '#toc-content',
            contentSelector: '#articleContent',
            headingsOffset: -($(window).height() * 0.4 - 45),
            collapseDepth: Number('0'),
            headingSelector: 'h2, h3, h4'
        });

        // modify the toc link href to support Chinese.
        let i = 0;
        let tocHeading = 'toc-heading-';
        $('#toc-content a').each(function () {
            $(this).attr('href', '#' + tocHeading + (++i));
        });

        // modify the heading title id to support Chinese.
        i = 0;
        $('#articleContent').children('h2, h3, h4').each(function () {
            $(this).attr('id', tocHeading + (++i));
        });

        // Set scroll toc fixed.
        let tocHeight = parseInt($(window).height() * 0.4 - 64);
        let $tocWidget = $('.toc-widget');
        $(window).scroll(function () {
            let scroll = $(window).scrollTop();
            /* add post toc fixed. */
            if (scroll > tocHeight) {
                $tocWidget.addClass('toc-fixed');
            } else {
                $tocWidget.removeClass('toc-fixed');
            }
        });

        
        /* 修复文章卡片 div 的宽度. */
        let fixPostCardWidth = function (srcId, targetId) {
            let srcDiv = $('#' + srcId);
            if (srcDiv.length === 0) {
                return;
            }

            let w = srcDiv.width();
            if (w >= 450) {
                w = w + 21;
            } else if (w >= 350 && w < 450) {
                w = w + 18;
            } else if (w >= 300 && w < 350) {
                w = w + 16;
            } else {
                w = w + 14;
            }
            $('#' + targetId).width(w);
        };

        // 切换TOC目录展开收缩的相关操作.
        const expandedClass = 'expanded';
        let $tocAside = $('#toc-aside');
        let $mainContent = $('#main-content');
        $('#floating-toc-btn .btn-floating').click(function () {
            if ($tocAside.hasClass(expandedClass)) {
                $tocAside.removeClass(expandedClass).hide();
                $mainContent.removeClass('l9');
            } else {
                $tocAside.addClass(expandedClass).show();
                $mainContent.addClass('l9');
            }
            fixPostCardWidth('artDetail', 'prenext-posts');
        });
        
    });
</script>

    

</main>




    <footer class="page-footer bg-color">
    
        <link rel="stylesheet" href="/libs/aplayer/APlayer.min.css">
<style>
    .aplayer .aplayer-lrc p {
        
        display: none;
        
        font-size: 12px;
        font-weight: 700;
        line-height: 16px !important;
    }

    .aplayer .aplayer-lrc p.aplayer-lrc-current {
        
        display: none;
        
        font-size: 15px;
        color: #42b983;
    }

    
    .aplayer.aplayer-fixed.aplayer-narrow .aplayer-body {
        left: -66px !important;
    }

    .aplayer.aplayer-fixed.aplayer-narrow .aplayer-body:hover {
        left: 0px !important;
    }

    
</style>
<div class="">
    
    <div class="row">
        <meting-js class="col l8 offset-l2 m10 offset-m1 s12"
                   server="netease"
                   type="playlist"
                   id="503838841"
                   fixed='true'
                   autoplay='false'
                   theme='#42b983'
                   loop='all'
                   order='random'
                   preload='auto'
                   volume='0.7'
                   list-folded='true'
        >
        </meting-js>
    </div>
</div>

<script src="/libs/aplayer/APlayer.min.js"></script>
<script src="https://cdn.jsdelivr.net/npm/meting@2/dist/Meting.min.js"></script>

    
    <div class="container row center-align" style="margin-bottom: 0px !important;">
        <div class="col s12 m8 l8 copy-right">
            Copyright&nbsp;&copy;
            
                <span id="year">2021</span>
            
            <span id="year">2021</span>
            <a href="/about" target="_blank">lxx</a>
            |&nbsp;Powered by&nbsp;<a href="https://hexo.io/" target="_blank">Hexo</a>
            |&nbsp;Theme&nbsp;<a href="https://github.com/blinkfox/hexo-theme-matery" target="_blank">Matery</a>
            <br>
            
            &nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
                class="white-color">272.8k</span>&nbsp;字
            
            
            
            
            
            
            <span id="busuanzi_container_site_pv">
                |&nbsp;<i class="far fa-eye"></i>&nbsp;总访问量:&nbsp;<span id="busuanzi_value_site_pv"
                    class="white-color"></span>&nbsp;次
            </span>
            
            
            <span id="busuanzi_container_site_uv">
                |&nbsp;<i class="fas fa-users"></i>&nbsp;总访问人数:&nbsp;<span id="busuanzi_value_site_uv"
                    class="white-color"></span>&nbsp;人
            </span>
            
            <br>
            
            <br>
            
        </div>
        <div class="col s12 m4 l4 social-link social-statis">
    <a href="https://github.com/xinxinliang" class="tooltipped" target="_blank" data-tooltip="访问我的GitHub" data-position="top" data-delay="50">
        <i class="fab fa-github"></i>
    </a>



    <a href="mailto:1974733812@qq.com" class="tooltipped" target="_blank" data-tooltip="邮件联系我" data-position="top" data-delay="50">
        <i class="fas fa-envelope-open"></i>
    </a>







    <a href="tencent://AddContact/?fromId=50&fromSubId=1&subcmd=all&uin=1974733812" class="tooltipped" target="_blank" data-tooltip="QQ联系我: 1974733812" data-position="top" data-delay="50">
        <i class="fab fa-qq"></i>
    </a>







    <a href="/atom.xml" class="tooltipped" target="_blank" data-tooltip="RSS 订阅" data-position="top" data-delay="50">
        <i class="fas fa-rss"></i>
    </a>

</div>
    </div>
</footer>

<div class="progress-bar"></div>


    <!-- 搜索遮罩框 -->
<div id="searchModal" class="modal">
    <div class="modal-content">
        <div class="search-header">
            <span class="title"><i class="fas fa-search"></i>&nbsp;&nbsp;搜索</span>
            <input type="search" id="searchInput" name="s" placeholder="请输入搜索的关键字"
                   class="search-input">
        </div>
        <div id="searchResult"></div>
    </div>
</div>

<script type="text/javascript">
$(function () {
    var searchFunc = function (path, search_id, content_id) {
        'use strict';
        $.ajax({
            url: path,
            dataType: "xml",
            success: function (xmlResponse) {
                // get the contents from search data
                var datas = $("entry", xmlResponse).map(function () {
                    return {
                        title: $("title", this).text(),
                        content: $("content", this).text(),
                        url: $("url", this).text()
                    };
                }).get();
                var $input = document.getElementById(search_id);
                var $resultContent = document.getElementById(content_id);
                $input.addEventListener('input', function () {
                    var str = '<ul class=\"search-result-list\">';
                    var keywords = this.value.trim().toLowerCase().split(/[\s\-]+/);
                    $resultContent.innerHTML = "";
                    if (this.value.trim().length <= 0) {
                        return;
                    }
                    // perform local searching
                    datas.forEach(function (data) {
                        var isMatch = true;
                        var data_title = data.title.trim().toLowerCase();
                        var data_content = data.content.trim().replace(/<[^>]+>/g, "").toLowerCase();
                        var data_url = data.url;
                        data_url = data_url.indexOf('/') === 0 ? data.url : '/' + data_url;
                        var index_title = -1;
                        var index_content = -1;
                        var first_occur = -1;
                        // only match artiles with not empty titles and contents
                        if (data_title !== '' && data_content !== '') {
                            keywords.forEach(function (keyword, i) {
                                index_title = data_title.indexOf(keyword);
                                index_content = data_content.indexOf(keyword);
                                if (index_title < 0 && index_content < 0) {
                                    isMatch = false;
                                } else {
                                    if (index_content < 0) {
                                        index_content = 0;
                                    }
                                    if (i === 0) {
                                        first_occur = index_content;
                                    }
                                }
                            });
                        }
                        // show search results
                        if (isMatch) {
                            str += "<li><a href='" + data_url + "' class='search-result-title'>" + data_title + "</a>";
                            var content = data.content.trim().replace(/<[^>]+>/g, "");
                            if (first_occur >= 0) {
                                // cut out 100 characters
                                var start = first_occur - 20;
                                var end = first_occur + 80;
                                if (start < 0) {
                                    start = 0;
                                }
                                if (start === 0) {
                                    end = 100;
                                }
                                if (end > content.length) {
                                    end = content.length;
                                }
                                var match_content = content.substr(start, end);
                                // highlight all keywords
                                keywords.forEach(function (keyword) {
                                    var regS = new RegExp(keyword, "gi");
                                    match_content = match_content.replace(regS, "<em class=\"search-keyword\">" + keyword + "</em>");
                                });

                                str += "<p class=\"search-result\">" + match_content + "...</p>"
                            }
                            str += "</li>";
                        }
                    });
                    str += "</ul>";
                    $resultContent.innerHTML = str;
                });
            }
        });
    };

    searchFunc('/search.xml', 'searchInput', 'searchResult');
});
</script>

    <!-- 回到顶部按钮 -->
<div id="backTop" class="top-scroll">
    <a class="btn-floating btn-large waves-effect waves-light" href="#!">
        <i class="fas fa-arrow-up"></i>
    </a>
</div>


    <script src="/libs/materialize/materialize.min.js"></script>
    <script src="/libs/masonry/masonry.pkgd.min.js"></script>
    <script src="/libs/aos/aos.js"></script>
    <script src="/libs/scrollprogress/scrollProgress.min.js"></script>
    <script src="/libs/lightGallery/js/lightgallery-all.min.js"></script>
    <script src="/js/matery.js"></script>

    <!-- Baidu Analytics -->

    <!-- Baidu Push -->

<script>
    (function () {
        var bp = document.createElement('script');
        var curProtocol = window.location.protocol.split(':')[0];
        if (curProtocol === 'https') {
            bp.src = 'https://zz.bdstatic.com/linksubmit/push.js';
        } else {
            bp.src = 'http://push.zhanzhang.baidu.com/push.js';
        }
        var s = document.getElementsByTagName("script")[0];
        s.parentNode.insertBefore(bp, s);
    })();
</script>

    
    <script src="/libs/others/clicklove.js" async="async"></script>
    
    
    <script async src="/libs/others/busuanzi.pure.mini.js"></script>
    

    

    
    <script>
        (function (i, s, o, g, r, a, m) {
            i["DaoVoiceObject"] = r;
            i[r] = i[r] || function () {
                (i[r].q = i[r].q || []).push(arguments)
            }, i[r].l = 1 * new Date();
            a = s.createElement(o), m = s.getElementsByTagName(o)[0];
            a.async = 1;
            a.src = g;
            a.charset = "utf-8";
            m.parentNode.insertBefore(a, m)
        })(window, document, "script", ('https:' == document.location.protocol ? 'https:' : 'http:') +
            "//widget.daovoice.io/widget/6984b559.js", "daovoice")
        daovoice('init', {
            app_id: "7b318e23"
        });
        daovoice('update');
    </script>
    

    <!--腾讯兔小巢-->
    
    

    

    

    
    <script src="/libs/instantpage/instantpage.js" type="module"></script>
    

</body>

</html>
